Given that $I_{0}=10^{-12}$ watts/meter ${ }^{2}$, what is the intensity of a sound for which the decibel level of the sound measures 139 ? Round off your answer to three decimal places. Keypad Answer gens in new window) Keybard Shortcuts watts/meter ${ }^{2}$

Step 1 ：The decibel level of a sound is given by the formula: \(dB = 10 \cdot \log_{10}(I/I_{0})\), where \(dB\) is the decibel level, \(I\) is the intensity of the sound, and \(I_{0}\) is the reference intensity, which is given as \(10^{-12}\) watts/meter\(^{2}\).

Step 2 ：We are given that \(dB = 139\), and we need to find \(I\). We can rearrange the formula to solve for \(I\): \(I = I_{0} \cdot 10^{(dB/10)}\).

Step 3 ：We can substitute the given values into this formula to find the intensity of the sound: \(I_{0} = 1e-12\), \(dB = 139\), \(I = 79.433\).

Step 4 ：Final Answer: The intensity of a sound for which the decibel level of the sound measures 139 is \(\boxed{79.433}\) watts/meter\(^{2}\).